Metamath Proof Explorer


Theorem 5p5e10

Description: 5 + 5 = 10. (Contributed by NM, 5-Feb-2007) (Revised by Stanislas Polu, 7-Apr-2020) (Revised by AV, 6-Sep-2021)

Ref Expression
Assertion 5p5e10 ⊢ 5 + 5 = 10

Proof

Step Hyp Ref Expression
1 df-5 ⊢ 5 = 4 + 1
2 1 oveq2i ⊢ 5 + 5 = 5 + 4 + 1
3 5cn ⊢ 5 ∈ ℂ
4 4cn ⊢ 4 ∈ ℂ
5 ax-1cn ⊢ 1 ∈ ℂ
6 3 4 5 addassi ⊢ 5 + 4 + 1 = 5 + 4 + 1
7 2 6 eqtr4i ⊢ 5 + 5 = 5 + 4 + 1
8 5p4e9 ⊢ 5 + 4 = 9
9 8 oveq1i ⊢ 5 + 4 + 1 = 9 + 1
10 9p1e10 ⊢ 9 + 1 = 10
11 7 9 10 3eqtri ⊢ 5 + 5 = 10